Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena by Alexa

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Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena by Alexander N. Gorban, Nikolas Kazantzis, I.G. Kevrekidis, Konstantinos Theodoropoulos, Hans Christian Öttinger

Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.

Back Cover

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.

Table of Contents

Computation of Invariant Manifolds.- A New Model Reduction Method for Nonlinear Dynamical Systems Using Singular PDE Theory.- A Versatile Algorithm for Computing Invariant Manifolds.- Covering an Invariant Manifold with Fat Trajectories.- "Ghost" ILDM-Manifolds and Their Identification.- Dynamic Decomposition of ODE Systems: Application to Modelling of Diesel Fuel Sprays.- Model Reduction of Multiple Time Scale Processes in Non-standard Singularly Perturbed Form.- Coarse-Graining and Ideas of Statistical Physics.- Basic Types of Coarse-Graining.- Renormalization Group Methods for Coarse-Graining of Evolution Equations.- A Stochastic Process Behind Boltzmann's Kinetic Equation and Issues of Coarse Graining.- Finite Difference Patch Dynamics for Advection Homogenization Problems.- Coarse-Graining the Cyclic Lotka-Volterra Model: SSA and Local Maximum Likelihood Estimation.- Relations Between Information Theory, Robustness and Statistical Mechanics of Stochastic Uncertain Systems via Large Deviation Theory.- Kinetics and Model Reduction.- Exactly Reduced Chemical Master Equations.- Model Reduction in Kinetic Theory.- Novel Trajectory Based Concepts for Model and Complexity Reduction in (Bio)Chemical Kinetics.- Dynamics of the Plasma Sheath.- Mesoscale and Multiscale Modeling.- Construction of Stochastic PDEs and Predictive Control of Surface Roughness in Thin Film Deposition.- Lattice Boltzmann Method and Kinetic Theory.- Numerical and Analytical Spatial Coupling of a Lattice Boltzmann Model and a Partial Differential Equation.- Modelling and Control Considerations for Particle Populations in Particulate Processes Within a Multi-Scale Framework.- Diagnostic Goal-Driven Reduction of Multiscale Process Models.- Understanding Macroscopic Heat/Mass Transfer Using Meso-and Macro-Scale Simulations.- An Efficient Optimization Approach for Computationally Expensive Timesteppers Using Tabulation.- A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems.

Long Description

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.

Feature

Dealing with systems with many degrees of freedom and how they can be mathematically described in a way to manage the variety, this book explains how macroscopic properties arise from microscopic and nano-properties.

Details ISBN3540358854 Short Title MODEL REDUCTION & COARSE-GRAIN Pages 560 Series Springer Complexity Language English ISBN-10 3540358854 ISBN-13 9783540358855 Media Book Format Hardcover Year 2006 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 530.15 Edited by Hans Christian Öttinger Affiliation University of Leicester Edition 2006th DOI 10.1604/9783540358855 Author Hans Christian Öttinger Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2006 ed. Publication Date 2006-08-24 Illustrations XI, 560 p. Audience Professional & Vocational Country of Origin DE Product Class Description Engineering & Technology: Textbooks & Study Guides Alternative 9783540358886
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